Critical behavior and anisotropic magnetocaloric effect of the quasi-one-dimensional hexagonal ferromagnet Pr Cr Ge 3

Critical properties and anisotropic magnetocaloric effect of hexagonal ferromagnet $\\mathrm{Pr}\\mathrm{Cr}{\\mathrm{Ge}}_{3}$ single crystals were investigated. The critical exponents $\\ensuremath{\\beta}=0.352$ with a critical temperature ${T}_{C}=90.5\\phantom{\\rule{0.28em}{0ex}}\\mathrm{K}$ and $\\ensuremath{\\gamma}=1.026$ with ${T}_{C}=90.6\\phantom{\\rule{0.28em}{0ex}}\\mathrm{K}$ are obtained by the modified Arrott plot, whereas $\\ensuremath{\\delta}=3.98$ is deduced by a critical isotherm analysis. The critical exponents suggest a long-range magnetic coupling with the exchange distance decaying as $J(r)\\ensuremath{\\sim}{r}^{\\ensuremath{-}4.6}$. Furthermore, the magnetic entropy change $\\ensuremath{-}\\mathrm{\\ensuremath{\\Delta}}{S}_{M}$ reaches a maximum value around ${T}_{C}$, i.e., $\\ensuremath{-}\\mathrm{\\ensuremath{\\Delta}}{S}_{M}\\ensuremath{\\sim}3.2(1.8)\\phantom{\\rule{0.28em}{0ex}}\\mathrm{J}\\phantom{\\rule{0.28em}{0ex}}{\\mathrm{kg}}^{\\ensuremath{-}1}\\phantom{\\rule{0.16em}{0ex}}{\\mathrm{K}}^{\\ensuremath{-}1}$ with in-plane (out-of-plane) field change of 5 T, verifying large magnetic anisotropy. The rescaled $\\ensuremath{-}\\mathrm{\\ensuremath{\\Delta}}{S}_{M}(T,H)$ plots collapse onto a universal curve independent of temperature and field, confirming a second-order magnetic phase transition and reliability of the obtained critical exponents.